Temperature effects on microwave-induced resistivity oscillations and zero resistance states in 2D electron systems

In this work we address theoretically a key issue concerning microwave-induced longitudinal resistivity oscillations and zero resistance states, as is tempoerature. In order to explain the strong temperature dependence of the longitudinal resistivity and the thermally activated transport in 2DEG, we have developed a microscopic model based on the damping suffered by the microwave-driven electronic orbit dynamics by interactions with the lattice ions yielding acoustic phonons. Recent experimental results show a reduction in the amplitude of the longitudinal resistivity oscillations and a breakdown of zero resistance states as the radiation intensity increases. In order to explain it we have included in our model the electron heating due to large microwave intensities and its effect on the longitudinal resistivity.Comment: 4 pages and 4 figures. Accepted in Phys Rev

Approximations from Anywhere and General Rough Sets

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \emph{Granular operator spaces} have been recently introduced and investigated by the present author in her recent work in the context of antichain based and dialectical semantics for general rough sets. The nature of the inverse problem is examined from number-theoretic and combinatorial perspectives in a higher order variant of granular operator spaces and some necessary conditions are proved. The results and the novel approach would be useful in a number of unsupervised and semi supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings, Springe

AN OPERATIONAL APPROACH FOR EVALUATING INVESTMENT RISK: AN APPLICATION TO THE NO-TILL TRANSITION

This study analyses short and long term safety first business risk associated with twenty six no-till transition strategies across four types of farms in eastern Washington. Risk of transition failure generated from risk averse criteria are also contrasted with a risk neutral criterion. Results revealed (1) that speeds of adoption have a larger effect than drill acquisition sequences in successful transition, (2) high equity farm have higher chance of success, and (3) slow acreage expansion with a custom or rental drill is preferred until yield penalty is eliminated.Farm Management, Risk and Uncertainty,

(k,q)-Compressed Sensing for dMRI with Joint Spatial-Angular Sparsity Prior

Advanced diffusion magnetic resonance imaging (dMRI) techniques, like diffusion spectrum imaging (DSI) and high angular resolution diffusion imaging (HARDI), remain underutilized compared to diffusion tensor imaging because the scan times needed to produce accurate estimations of fiber orientation are significantly longer. To accelerate DSI and HARDI, recent methods from compressed sensing (CS) exploit a sparse underlying representation of the data in the spatial and angular domains to undersample in the respective k- and q-spaces. State-of-the-art frameworks, however, impose sparsity in the spatial and angular domains separately and involve the sum of the corresponding sparse regularizers. In contrast, we propose a unified (k,q)-CS formulation which imposes sparsity jointly in the spatial-angular domain to further increase sparsity of dMRI signals and reduce the required subsampling rate. To efficiently solve this large-scale global reconstruction problem, we introduce a novel adaptation of the FISTA algorithm that exploits dictionary separability. We show on phantom and real HARDI data that our approach achieves significantly more accurate signal reconstructions than the state of the art while sampling only 2-4% of the (k,q)-space, allowing for the potential of new levels of dMRI acceleration.Comment: To be published in the 2017 Computational Diffusion MRI Workshop of MICCA

How Dirac's Seminal Contributions Pave the Way for Comprehending Nature's Deeper Designs

Credible reasons are presented to reveal that many of the lingering century old enigmas, surrounding the behavior of at least an individual quantum particle, can be comprehended in terms of an objectively real specific wave function. This wave function is gleaned from the single particle energy-momentum eigenstate offered by the theory of space filling universal quantum fields that is an inevitable outcome of Dirac's pioneering masterpiece. Examples of these well-known enigmas are wave particle duality, the de Broglie hypothesis, the uncertainty principle, wave function collapse, and predictions of measurement outcomes in terms of probability instead of certainty. Paul Dirac successfully incorporated special theory of relativity into quantum mechanics for the first time. This was accomplished through his ingenious use of matrices that allowed the equations of motion to maintain the necessary first order time derivative feature necessary for positive probability density. The ensuing Dirac equation for the electron led to the recognition of the mystifying quantized spin and magnetic moment as intrinsic properties in contrast to earlier ad hoc assumptions. The solution of his relativistic equation for the hydrogen atom produced results in perfect agreement with experimental data available at the time. The most far reaching prediction of the celebrated Dirac equation was the totally unexpected existence of anti-particles, culminating in the eventual development of the quantum field theory of the Standard Model that reveals the deepest secrets of the universe known to date.Quanta 2019; 8: 88–100

Deciphering the Enigma of Wave-Particle Duality

A satisfactory explanation of the confounding wave-particle duality of matter is presented in terms of the reality of the wave nature of a particle. In this view, a quantum particle is an objectively real wave packet consisting of irregular disturbances of underlying quantum fields. It travels holistically as a unit and thereby acts as a particle. Only the totality of the entire wave packet at any instance embodies all the conserved quantities, for example the energy-momentum, rest mass, and charge of the particle, and as such must be acquired all at once during detection. On this basis, many of the bizarre behaviors observed in the quantum domain, such as wave function collapse, the limitation of prediction to only a probability rather than an actuality, the apparent simultaneous existence of a particle in more than one place, and the inherent uncertainty can be reasonably comprehended. The necessity of acquiring the wave function in its entirety for detection, as evinced by the appearance of collapse of the wave function, supports the paradigm of reality of the wave function described here.Quanta 2016; 5: 93–100

Is Schrödinger's Cat Alive?

Erwin Schrödinger is famous for presenting his wave equation of motion that jump-started quantum mechanics. His disenchantment with the Copenhagen interpretation of quantum mechanics led him to unveil the Schrödinger's cat paradox, which did not get much attention for nearly half a century. In the meantime, disappointment with quantum mechanics turned his interest to biology facilitating, albeit in a peripheral way, the revelation of the structure of DNA. Interest in Schrödinger's cat has recently come roaring back making its appearance conspicuously in numerous scientific articles. From the arguments presented here, it would appear that the legendary Schrödinger's cat is here to stay, symbolizing a profound truth that quantum reality exists at all scales; but we do not observe it in our daily macroscopic world as it is masked for all practical purposes, most likely by environmental decoherence with irreversible thermal effects.Quanta 2017; 6: 70–80

Was Albert Einstein Wrong on Quantum Physics?

Albert Einstein is considered by many physicists as the father of quantum physics in some sense. Yet there is an unshakable view that he was wrong on quantum physics. Although it may be a subject of considerable debate, the core of his allegedly wrong demurral was the insistence on finding an objective reality underlying the manifestly bizarre behavior of quantum objects. The uncanny wave-particle duality of a quantum particle is a prime example. In view of the latest developments, particularly in quantum field theory, the objections of Einstein are substantially corroborated. Careful investigation suggests that a travelling quantum particle is a holistic wave packet consisting of an assemblage of irregular disturbances in quantum fields. It acts as a particle because only the totality of all the disturbances in the wave packet yields the energy-momentum with the mass of a particle, along with its other conserved quantities such as charge and spin. Thus the wave function representing a particle is not just a fictitious mathematical construct but embodies a reality of nature as asserted by Einstein.Quanta 2015; 4: 35–42

Is the Quantum State Real in the Hilbert Space Formulation?

The persistent debate about the reality of a quantum state has recently come under limelight because of its importance to quantum information and the quantum computing community. Almost all of the deliberations are taking place using the elegant and powerful but abstract Hilbert space formalism of quantum mechanics developed with seminal contributions from John von Neumann. Since it is rather difficult to get a direct perception of the events in an abstract vector space, it is hard to trace the progress of a phenomenon. Among the multitude of recent attempts to show the reality of the quantum state in Hilbert space, the Pusey–Barrett–Rudolph theory gets most recognition for their proof. But some of its assumptions have been criticized, which are still not considered to be entirely loophole free. A straightforward proof of the reality of the wave packet function of a single particle has been presented earlier based on the currently recognized fundamental reality of the universal quantum fields. Quantum states like the atomic energy levels comprising the wave packets have been shown to be just as real. Here we show that an unambiguous proof of reality of the quantum states gleaned from the reality of quantum fields can also provide an explicit substantiation of the reality of quantum states in Hilbert space.Quanta 2020; 9: 37–46